The Bishop of Leeds has written to the Prime Minister in a strong attack backed by the Archbishop of Canterbury.
The Rt Revd Nicholas Baines told David Cameron 'many' senior clergy were seriously concerned by the situation in Iraq where IS fighters, formerly ISIS, have forced thousands of Christians to flee their homes.
The group is being accused of genocide actions by the United States.
Bishop Nicholas questioned whether the government had any long term strategy in Iraq and criticised a "growing silence" over the plight of persecuted Christians.
Some countries including France have offered asylum to believers who're facing persecution but Britain has not.
The Bishop said he has fears about the governments "commitment to religious freedom".
He said: "It appears that, in common with the United States and other partners, the UK is responding to events in a reactive way, and it is difficult to discern the strategic intentions behind this approach.
"Please can you tell me what is the overall strategy that holds together the UK Government's response to both the humanitarian situation and what IS is actually doing in Syria and Iraq?
"Behind this question is the serious concern that we do not seem to have a coherent or comprehensive approach to Islamist extremism as it is developing across the globe.
"Islamic State, Boko Haram and other groups represent particular manifestations of a global phenomenon, and it is not clear what our broader global strategy is - particularly insofar as the military, political, economic and humanitarian demands interconnect."
He added that the focus on helping the Yazidi community, who have been at the centre of an international aid operation as they flee IS massacres, was "notable and admirable" but raised concerns about the help offered to Christians.
"However, there has been increasing silence about the plight of tens of thousands of Christians who have been displaced, driven from cities and homelands, and who face a bleak future," he said.
"Despite appalling persecution, they seem to have fallen from consciousness, and I wonder why.
"Does your government have a coherent response to the plight of these huge numbers of Christians whose plight appears to be less regarded than that of others? Or are we simply reacting to the loudest media voice at any particular time?" He added.
On Premier's News Hour the Bishop of Warwick, the Rt Revd John Stroyan, refused to criticise the government.
"David Cameron needs all the support and prayers we can give him," he said.
He added: "He's absolutely right to be doing a lot in terms of humanitarian aid."
But Bishop John did say he would support some sort of military action on the ground: "My own preference would be for a UN force because that would have less of an inflammatory dimension than a force that could be perceived as Western Christian." He said.
Meanwhile Iraqi and Kurdish forces have reportedly pushed back Islamist extremists from a key site in the north of the country.
US airstrikes allowed troops to apparently seize control of the Mosul Dam.
British warplanes are still involved in a humanitarian role, as David Cameron has insisted the UK is not getting dragged into another war.
Hear more from the Bishop of Warwick, the Rt Revd John Stroyan, here: